Find the height of the cone.

Question

The value of the surface area (in square centimeters) of the cone is equal to the value of the volume (in cubic centimeter) of the cone. The formula for the surface area S of a right cone is S=3.14(r)(r)+3.14(r)(l), where r is the radius of the base and l is the slant height. The radius of the cone is 5cm and the slant height is 12cm.

Answer 1

S = πr² + πrL  V = (1/3)πr²h

 

Since S = V, π(5)² + π(5)(12) = (1/3)π(5)²h

 

                   85 = (25/3)h

 

                    h = 85(3/25) = 10.2 cm